Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions
نویسندگان
چکیده
منابع مشابه
Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions
This paper examines the bifurcation and structure of the bifurcated solutions of the two-dimensional infinite Prandtl number convection problem. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [14]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and that it is homeomorphic to S1. By thor...
متن کاملStructure of bifurcated solutions of two-dimensional infinite Prandtl number convection with no-slip boundary conditions
We consider the two-dimensional infinite Prandtl number convection problem with no-slip boundary conditions. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [15]. The no-stress case has been examined in [16]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and it is homeomorphic to S. By ...
متن کاملAddendum to the Paper ”two-dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions, J.
The main objective of this addendum to the mentioned article [49] by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to comment and list some related literatures, without any intention to provide a complete survey. For steady state PDE bifurcation problems, the often used c...
متن کاملBifurcation of Infinite Prandtl Number Rotating Convection
We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...
متن کاملEffects of vertical boundaries on infinite Prandtl number thermal convection
The physics of thermomechanical coupling of the continental lithosphere and its surrounding mantle is studied using a simple hydrodynamic model in which a fluid is heated from below and is bounded by rigid side walls. Rayleigh numbers up to 10 are considered. A series of finite-element stability analyses is employed to characterize systematically the nature of convective instability in such a s...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2007
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-005-0747-9